New Results on Tracking and Adaptive Tracking Control of High-Order Nonlinear Systems with Polynomial Conditions

Many practical dynamical models are inherently nonlinear and may exhibit complex growth conditions and uncertainties, which pose considerable challenges to controller design. In this paper, the tracking control issue for a category of high-order nonlinear systems with polynomial-type growth conditions is studied. Through the construction of a new Lyapunov function and the development of a dynamic-gain-based homogeneous control method, a robust tracking controller is designed to achieve the required tracking accuracy while ensuring the global boundedness of all closed-loop signals. As an extension, the system with unknown nonlinear functions is further considered, and a new adaptive tracking controller is constructed. Simulation examples demonstrate the efficacy of the presented control methods.